18.417: lecture 2

Brute force and digest problems

For class:Problem set 1 is out

Enzyme activity works to destroy foreign DNA

Lengths of DNA fragments can be measured:

The goal in restriction mapping is be able to find the order of the fragments, knowing just the fragment lengths.

Full restriction digest

Partial restriction digest

Idea: a piece of DNA is digested by a restriction enzyme, resulting in a multiset of fragments, one fragment per pair of restriction sites.
Idealizations: we can control digestion enough to guarantee that every possible fragment will be produced, and we can count the multiplicity of fragments of with the same length.
Input: a multiset of fragments resulting from the ideal partial digestion of a piece of DNA.
Output: a set of restriction site locations and endpoints which gives rise to the same multiset of fragments.

input: L = {3,5,5,8,9,14,14,17,19,22}

output: X = {0,5,14,19,23}, endpoints at 0 and 23 with sites at 5,14,19.

digestion:

The two sets {0,1,2,5,7,9,12} and {0,1,5,7,8,10,12} digest to the same thing

The multiset {1,1,2,2,2,3,3,4,4,5,5,5,6,7,7,7,8,9,10,11,12}

Idea: an easier laboratory experiment is to digest the same DNA with two different enzymes, resulting in 3 fragment sets.
Idealizations: still requires that we can know the multiplicity of fragments of with the same length.
Input: 3 multisets of fragments resulting from the ideal double digestion of a single piece of DNA.
Output: a set of restriction site locations and endpoints for the two enzymes, which gives rise to the same multisets of fragments.

Sites A = {173,201,315,512,526,526,557,619,776,777}

Sites B = {71,91,159,250,258,273,371,413,558,640}